Question

How do you convert $\dfrac{7}{9}$ to a decimal?

Answer 1

Hint:
Here we need to divide $7{\text{ by 9}}$ and we will get the quotient which will be repeating or recurring and therefore we can write in the form of the decimal with the bar on the number that is repeating.

Complete step by step solution:
Here we are given the fraction which is $\dfrac{7}{9}$ and we are given to find the decimal of this fraction. We know that in the fraction $\dfrac{7}{9}$ $7$ is the dividend and $9$ is the divisor and we need to find the quotient which means we need to find the number which when multiplied by $9{\text{ gives 7}}$.
Let us multiply the fraction in the numerator and denominator by $10$ and hence we will get:
The fraction becomes $\dfrac{7}{9} \times \dfrac{{10}}{{10}}$ and we can write it in the form of:
$\dfrac{{70}}{9} \times \dfrac{1}{{10}}$.
Now we can divide $70{\text{ by 9}}$ and then we can get the result of it and further divide that value obtained by $10$ to get the decimal value.
So we know that $70$ is not the exact multiple of $9$ so we need to see the number less than $70$ which is a multiple of $9$
As we know that
$
  (9)(7) = 63 \\
  (9)(8) = 72 \\
 $
Hence we can say that $63$ is the nearest small number that is divisible by $9$ completely. Hence we can divide and we will get $7$ before the decimal and the remainder we will get is $70 - 63 = 7$ now we can insert the decimal and apply zero after $7$ which is the previous quotient obtained and again we will get the same quotient which will be $7$ and goes on repeating and hence we can say that we will get the answer as $7.7777.....$.
Now we know this is the value of when we can divide $70{\text{ by 9}}$.
Now we need to put this value in $\dfrac{{70}}{9} \times \dfrac{1}{{10}}$ and we will get $\dfrac{{7.7777....}}{{10}}$.
So we know that when we divide any number with ${10^n}$ we only need to shift the decimal form right to left in the numerator till the $n{\text{th}}$ term from the right.
Here we have $\dfrac{{7.777....}}{{10}}$ as the fraction and we can compare the denominator with ${10^n}$so we get that $n = 1$ and therefore we need to move in numerator from right to left $n{\text{th}}$ term and then put decimal over there. So here when we move from right to left in the numerator which is \[1\] we get the result as $0.7777.....$ and as $7$ is repeating here we can put a bar over it and write it as $0.\overline 7 $.

Note:
Here the student must keep in mind that whenever we are given to find the decimal of the fraction which on solving keeps on repeating we need to put a bar sign on that number from where it has started repeating. For example: If we have the decimal $0.16666......$ then we would write it as $0.1\overline 6 $.